The present invention relates to water purification, and more particularly to flow through capacitors and capacitive deionization. It is known in the prior art to use an electrode assembly made from opposing pairs of oppositely chargeable high capacitance electrodes for the deionization or purification of water. This is known as a flow through capacitor, or capacitive deionization. Upon application of an electric potential or voltage to terminals connected to underlying current collectors, the electrodes develop a charge. Positively and negatively charged ions present in a water stream attract to and electrostatically adsorb onto the opposite polarity, negatively and positively charging electrodes, respectively, and are removed from solution to form a purified stream. This process is driven by a flow of electronic current due to non faradic capacitive charging. When the flow through capacitor is charged, it may be shunted or reversed in polarity in order to release the adsorbed ions in concentrated form. The purification and concentration streams may be diverted by a valve to a purified stream and a waste stream, in a series of alternating purification and concentration cycles.
A flow through capacitor is a capacitor of the so called “double layer type”. The double layer in this context of a capacitive charged electrode refers to the layers of electrostatic charge to which the ions attract and adsorb. These layers include a surface charge layer and a diffuse layer, also known as Stern and Guoy-Chapman layers. The characteristic length thickness of these layers comprising this so called double layer corresponds to the Debye length, also known as the Debye radius. This is estimated in Equation 1 as follows:
                              K                      -            1                          =                                                            ɛ                r                            ⁢                              ɛ                o                            ⁢                              k                b                            ⁢              T                                                      ∑                i                            ⁢                                                n                  i                                ⁢                                  z                  i                  2                                ⁢                                  e                  2                                                                                        Equation        ⁢                                  ⁢        1                            which for the example of a univalent salt reduces to        
      K          -      1        =                              ɛ          r                ⁢                  ɛ          o                ⁢                  k          b                ⁢        T                    2        ⁢                  N          A                ⁢                  e          2                ⁢        I                            Where        K−1 is the Debye length        εr is the dielectric constant of the solute        εo is the permittivity of free space        kb is Boltzman's constant        T is the absolute Temperature in Kelvins        e is the elementary charge        ni is the concentration of the i'th ionic species in numbers/m3         zi is the valence of the i'th ionic species        NA is Avogadro's number        I is the ionic concentration in the solute in moles/m3         
Capacitance increases with surface area, which in turn typically requires that the capacitor electrodes are porous and have a pore volume.
Equation 2 is the formula for the amount of the electrode pore volume which is occupied by the double layer in a given ionic feed solution and a given surface area charged porous electrode material.Pore volume occupied by the double layer=A*K−1,  Equation 2where A is the electrode material microscopic pore surface area. In this context, a microscopic electrode pore surface is a surface of the electrode pores, whether micro-, meso-, or macropores. Under some typical feed water conditions, the Debye length is of the same order of magnitude as the average pore radius in micro and meso porous capacitive deionization electrodes. Therefore the pore volume occupied by the double layer can constitute the majority proportion of the total pore volume. This Debye length defined double layer pore volume is the region across which the voltage, or potential difference, in the charged capacitor drops. This electrical potential difference is caused by the distribution of charges within the double layer resulting from the attraction, expulsion and adsorption of charged ions during the process of deionization.